Adaptation of Moreau-Yosida regularization to the modulus of convexity

Abstract

We study a generalization of Moreau-Yosida regularization that is adapted to the geometry of Banach spaces where the dual space is uniformly convex with modulus of convexity of power type. Important properties for regularized convex functions are given, in particular strong monotonicity of the subdifferential of their convex conjugate and Hölder-continuity of their gradient.

References in corpus (5)

• Differentiable but exact formulation of density-functional theory
• Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions
• Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
• Generalized Kohn-Sham iteration on Banach spaces
• On proximal mappings with Young functions in uniformly convex Banach spaces

Cited by in corpus (2)

• Regularised density-potential inversion for periodic systems: application to exact exchange in one dimension
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory